{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fac00510-2f6a-4af8-9eab-25c08fba2b99",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.fft import fft, fftfreq\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.polynomial.chebyshev import Chebyshev\n",
    "from numpy.polynomial.legendre import Legendre\n",
    "import math\n",
    "plt.rcParams['axes.unicode_minus']=False#用来正常显示负号\n",
    "plt.rcParams['font.sans-serif']=['SimHei']#用来正常显示中文标签\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "50561c6b-8a7e-43c8-8451-fe0e719de4f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# 定义函数\n",
    "def f(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "# 定义区间和点\n",
    "x = np.linspace(-10, 10, 100)\n",
    "y_real = f(x)\n",
    "\n",
    "# 切比雪夫逼近\n",
    "cheb_coeffs = Chebyshev.fit(x, f(x), 3).convert().coef  # 5阶切比雪夫多项式\n",
    "y_cheb = np.polynomial.chebyshev.chebval(x, cheb_coeffs)\n",
    "\n",
    "# 勒让德逼近\n",
    "leg_coeffs = Legendre.fit(x, f(x), 3).convert().coef  # 5阶勒让德多项式\n",
    "y_leg = np.polynomial.legendre.legval(x, leg_coeffs)\n",
    "\n",
    "# 绘图\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(x, y_real, label=\"Real $e^x$\", color='black', linewidth=2)\n",
    "plt.plot(x, y_cheb, '--', label=\"Chebyshev Approximation (5th)\", color='red')\n",
    "plt.plot(x, y_leg, '--', label=\"Legendre Approximation (5th)\", color='blue')\n",
    "plt.legend()\n",
    "plt.title(\"Comparison of Chebyshev and Legendre Approximations\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$f(x)$\")\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e2343136-49a0-47dd-a903-552d2f293527",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f1(x):\n",
    "    return np.piecewise(x, [x < 0, x >= 0], [lambda x: 1, lambda x: -1])  # 方波\n",
    "\n",
    "L = np.pi\n",
    "x = np.linspace(-L, L, 1000)\n",
    "y = f1(x)\n",
    "\n",
    "# 傅里叶逼近\n",
    "def fourier_approximation(x, n_terms):\n",
    "    approx = 0\n",
    "    for n in range(1, n_terms + 1, 2):  # 奇数项\n",
    "        approx += (4 / (n * np.pi)) * np.sin(n * x)\n",
    "    return approx\n",
    "\n",
    "y_approx = fourier_approximation(x, 10)\n",
    "\n",
    "# 绘图\n",
    "plt.plot(x, y, label=\"Original Function\")\n",
    "plt.plot(x, y_approx, label=\"Fourier Approximation (10 terms)\")\n",
    "plt.legend()\n",
    "plt.title(\"Fourier Approximation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4028b30f-9a79-48e8-8f68-8196a5c20861",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 500  # 数据点数\n",
    "T = 1.0 / 50.0  # 采样间隔\n",
    "x = np.linspace(0.0, N*T, N, endpoint=False)\n",
    "y = np.sin(10.0 * 2.0 * np.pi * x) + 0.5 * np.sin(20.0 * 2.0 * np.pi * x)\n",
    "\n",
    "# FFT\n",
    "yf = fft(y)\n",
    "xf = fftfreq(N, T)[:N//2]  # 只取正频部分\n",
    "\n",
    "# 绘图\n",
    "plt.plot(xf, 2.0/N * np.abs(yf[:N//2]))\n",
    "plt.title(\"FFT of the Signal\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b141e03d-0cbf-4924-898f-37f581da4d82",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4cbc217f-66cf-468a-8dff-414d6a14b9bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bernstein 多项式逼近结果: 2.4000000000000004\n"
     ]
    }
   ],
   "source": [
    "def bernstein_polynomial(k, n, a, b, x):\n",
    "    \"\"\"计算区间 [a, b] 上的 Bernstein 多项式 B_{k,n}(x)\"\"\"\n",
    "    coefficient = math.comb(n, k)  # 组合数\n",
    "    factor = ((x - a)**k * (b - x)**(n - k)) / (b - a)**n\n",
    "    return coefficient * factor\n",
    "\n",
    "def bernstein_approximation(f, n, a, b, x):\n",
    "    \"\"\"计算区间 [a, b] 上的函数 f 的 Bernstein 逼近\"\"\"\n",
    "    approximation = 0\n",
    "    for k in range(n + 1):\n",
    "        x_k = a + k * (b - a) / n  # 节点\n",
    "        approximation += f(x_k) * bernstein_polynomial(k, n, a, b, x)\n",
    "    return approximation\n",
    "\n",
    "# 测试\n",
    "a, b = 0, 2  # 定义区间 [a, b]\n",
    "f = lambda x: x**2  # 被逼近函数\n",
    "n = 5  # Bernstein 多项式的次数\n",
    "x = 1.5  # 计算点\n",
    "result = bernstein_approximation(f, n, a, b, x)\n",
    "print(f\"Bernstein 多项式逼近结果: {result}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aa2a9e09-91ed-4622-99fb-9e9c8f2dc23e",
   "metadata": {},
   "outputs": [],
   "source": [
    "points = np.array([\n",
    "    [0, 0], \n",
    "    [1, 2], \n",
    "    [3, 3], \n",
    "    [6, 1], \n",
    "    [7, 0]\n",
    "])\n",
    "x, y = points[:, 0], points[:, 1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7e2eb74f-a538-4a8e-b758-fa8419f1a280",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 1])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diff(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "986c2958-bf68-4a3d-b332-024110ddd36f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 3, 6, 7])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b83f0c5-e534-4a4e-ad98-f84b3c5982f5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
